Question 1107725
the lighthouse and ship A and ship B make a right triangle as shown below:


that triangle is labeled ABC, where C is the position of the lighthouse.


from ship B, the bearing to the lighthouse is north 63 degrees 20 minutes east.


63 degrees 20 minutes is equal to 63 and 1/3 degrees because 20 seconds / 60 = 1/3 minutes.


that angle is shown in the following diagram.


<img src = "http://theo.x10hosting.com/2018/012803.jpg" alt="$$$" >


tangent of 63 and 1/3 degrees is equal to opposite side divided by adjacent side.


that makes tangent of 63 and 1/3 degrees = x / 12.


multiply both sides of this equation by 12 to get 12 * tan(63 and 1/3) = x


solve for x to get x = 23.89396451


here's a reference on bearing you might find helpful.


<a href = "http://www.mathsteacher.com.au/year10/ch15_trigonometry/11_directions/23dir.htm" target = "_blank">http://www.mathsteacher.com.au/year10/ch15_trigonometry/11_directions/23dir.htm<a>


your north line in the diagram is represented by the line segment AB.